Random Sampling Estimation Research Articles

Monitoring tropical forest change using tree canopy cover time series obtained from Sentinel-1 and Sentinel-2 data

ABSTRACT The most practical method for monitoring forest change over large areas is using remotely sensed data. However, given that current techniques are somewhat weak for monitoring small-scale forest disturbances, achieving accurate monitoring remains challenging, especially in tropical areas where selective and illegal logging occurs frequently. To further improve the ability to monitor forest changes, we estimated tree canopy cover (TCC) using Sentinel-1 and Sentinel-2 data. We developed an approach to monitor forest change on the obtained TCC time series. This approach was applied to monitor forest change in the Bago Mountains of Myanmar from 2017 to 2021. We then completed accuracy assessments and area estimation using reference data obtained from stratified random sampling and unbiased estimators. The final results indicated that: (1) in TCC estimation, Sentinel-1 played a limited role; the red-edge bands of Sentinel-2 achieved slightly different results to the other bands, and superior results were obtained by using all bands; (2) our method successfully mapped forest change with the overall accuracy of 93%. Furthermore, compared with the most widely used and the most recent approaches, our method was better at capturing forest disturbances.

Ratio estimation of two population means in two-phase stratified random sampling under a scrambled response situation

In this paper, we have described the development of an effective two-phase stratified random sampling estimation procedure in a scrambled response situation. Two different exponential, regression-type estimators were formed separately for different structures of two-phase stratified sampling schemes. We have studied the properties of the suggested strategy. The performance of the proposed strategy has been demonstrated through numerical evidence based on a data set of a natural population and a population generated through simulation studies. Taking into consideration the encouraging findings, suitable recommendations for survey statisticians are prepared for the application of the proposed strategy in real-life conditions.

Estimating the Population Mean in Stratified Random Sampling Using Combined Regression with the Presence of Outliers

In this research, the covariance estimates were used to estimate the population mean in the stratified random sampling and combined regression estimates. were compared by employing the robust variance-covariance matrices estimates with combined regression estimates by employing the traditional variance-covariance matrices estimates when estimating the regression parameter, through the two efficiency criteria (RE) and mean squared error (MSE). We found that robust estimates significantly improved the quality of combined regression estimates by reducing the effect of outliers using robust covariance and covariance matrices estimates (MCD, MVE) when estimating the regression parameter. In addition, the results of the simulation study proved that the Minimum covariance determinant (MCD) method is highly efficient at all sample sizes (n=35, 75, 150, 200, 500) and then followed by the method of the smallest ellipse Minimum volume Ellipsoid (MVE) handles outliers in the dataset, where it has lower values (MSE).

Optimization of chemically amplified resist formulation based on simple random sampling and kernel density estimation

Formulation optimization plays an important role in the research and development of chemically amplified resist (CAR). However, the CAR profile after development process is influenced by multiple resist parameters and process conditions, so it is hard to determine the optimal CAR formulation in the multivariate problem. An optimization method for the CAR formulation is developed. The simple random sampling is applied to each CAR parameter’s value range independently, and the combinations of these samples from different parameters are used in the simulation of lithography profiles. Kernel density estimation is applied to analyze the simulation results. Then the CAR formulation is optimized based on the probability density distribution from the analysis results. The verification results show that the proposed optimization method can greatly improve the stability of the CAR formulation and thus generating acceptable critical features’ sizes of the CAR profile.

Efficient Estimation of Two-Parameter Xgamma Distribution Parameters Using Ranked Set Sampling Design

An efficient method such as ranked set sampling is used for estimating the population parameters when the actual observation measurement is expensive and complicated. In this paper, we consider the problem of estimating the two-parameter xgamma (TPXG) distribution parameters under the ranked set sampling as well as the simple random sampling design. Various estimation methods, including the weighted least-square estimator, maximum likelihood estimators, least-square estimator, Cramer–von Mises, the maximum product of spacings estimators, and Anderson–Darling estimators, are considered. A comparison between the ranked set sampling and simple random sampling estimators, with the same number of measurement units, is conducted using a simulation study in terms of the bias, mean squared errors, and efficiency of estimators. The merit of the ranked set sampling estimators is examined using real data of bank customers. The results indicate that estimations using the ranked set sampling method are more efficient than the simple random sampling competitor considered in this study.

Triangle Sampling Based Estimation of Average Degree of Network Using Different Estimator

Graph are use to represent complex relationship which includes online social network, pandemic spread network and other real world networks. In recent time, graph sampling is used for study of different parameters of network, such includes many sampling algorithms like Random node, Random edge sampling, Rank degree, etc. which are used for collection of subset of network, but efficient estimation methods are not discussed much for parameter estimation. This paper presents a comparison of different estimators comprises Simple random sampling, Ratio and Regression estimator to estimate the average degree of network. To collect sample technique of triangles are collected using seed nodes. A comparative procedure is used to obtain the lower and upper limit of confidence intervals with the help of multiple samples. Ogive based simulation is also used for single value computation of both limits of confidence interval(CI). The results obtained from simulation, show that Regression estimator is more efficient than the Ratio and Simple random sampling based estimators.

Comparison of Variance Estimators for Systematic Environmental Sample Surveys: Considerations for Post-Stratified Estimation

The estimation of the sampling variance of point estimators under two-dimensional systematic sampling designs remains a challenge, and several alternative variance estimators have been proposed in the past few decades. In this work, we compared six alternative variance estimators under Horvitz-Thompson (HT) and post-stratification (PS) point estimation regimes. We subsampled a multitude of species-specific forest attributes from a large, spatially balanced national forest inventory to compare the variance estimators. A variance estimator that assumes a simple random sampling design exhibited positive relative bias under both HT and PS point estimation regimes ranging between 1.23 to 1.88 and 1.11 to 1.78 for HT and PS, respectively. Alternative estimators reduced this positive bias with relative biases ranging between 1.01 to 1.66 and 0.90 to 1.64 for HT and PS, respectively. The alternative estimators generally obtained improved efficiencies under both HT and PS, with relative efficiency values ranging between 0.68 to 1.28 and 0.68 to 1.39, respectively. We identified two estimators as promising alternatives that provide clear improvements over the simple random sampling estimator for a wide variety of attributes and under HT and PS estimation regimes.

Network representation using graph root distributions

Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work, we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes are independent random vectors in a linear space equipped with an indefinite inner product, and the edge probability between two nodes equals the inner product of the corresponding node vectors. Therefore, the distribution of exchangeable random graphs in this subclass can be represented by a node sampling distribution on this linear space, which we call the graph root distribution. We study existence and identifiability of such representations, the topological relationship between the graph root distribution and the exchangeable random graph sampling distribution and estimation of graph root distributions.

The role of workers' perceptions towards the uncertain result of ergonomic program

Manual activities of workers in palm oil factories cause pain complaints that can be resolved with an ergonomic program. However, the uncertainty of the success of the ergonomic program requires active involvement from workers. This study aims to discuss the role of workers’ perceptions towards the success of the ergonomic program intervention in palm oil mills. By referring to the theory of reasoned action and technology acceptance model, acceptance of workers to ergonomics programs are influenced by perceived usefulness, perceived ease of use, and perceived trust. All these research variables were analyzed simultaneously using Partial Least Squares Structural Equation Modeling (PLS-SEM) software, in which data were obtained from questionnaires given to 280 people working in 20 palm oil mills in North Sumatra Province. The sampling method used is simple random sampling and model estimation is performed using PLS regression algorithm and resampling bootstrapping method. The result shows that perceived usefulness has the biggest effect on the success of the ergonomic program, followed by perceived trust and perceived ease of use, which has a smaller effect. This study focuses on workers’ perception that needs to be considered for facing uncertain results in implementing an ergonomic program.

A Theoretical Inference About Ratio Estimation of Population Mean Using Ranked Set Sampling Under Bivariate Normal Distribution

Ranked set sampling is a sampling technique that uses ranking information when measuring units is difficult or expensive. In this study, ratio estimation of the population mean is considered in the case of units ranking by both auxiliary variable and the variable of interest in ranked set sampling under bivariate normal distribution. We obtained some theoretical inferences about the mean square error of the ratio estimation in this situation in a simple form depending on coefficient of variation. Besides, we made a theoretical comparison of mean square errors by ranking based on auxiliary variable and interested variable. Using this comparison, one can choose which ranking strategy should be utilized in a problem easily. The performance of the ratio estimators was compared by a simulation study. The simulation results indicated that the ranked set sampling estimators were more efficient than the simple random sampling estimators for the same sample size and correlation coefficient. A real data example was also given to demonstrate for calculating relative efficiencies.

Multi-matrix error estimation and reconciliation for quantum key distribution.

Post-processing is a significant step in quantum key distribution (QKD), which is used for correcting the quantum-channel noise errors and distilling identical corrected keys between two distant legitimate parties. Efficient error reconciliation protocol, which can lead to an increase in the secure key generation rate, is one of the main performance indicators of QKD setups. In this paper, we propose a multi-low-density parity-check codes based reconciliation scheme, which can provide remarkable perspectives for highly efficient information reconciliation. By testing our approach through data simulation, we show that the proposed scheme combining multi-syndrome-based error rate estimation allows for a more accurate estimation of the error rate as compared with random sampling and single-syndrome estimation techniques before the error correction, as well as a significant increase in the efficiency of the procedure without compromising security and sacrificing reconciliation efficiency.

A Double-Sampling Extension of the German National Forest Inventory for Design-Based Small Area Estimation on Forest District Levels

The German National Forest Inventory consists of a systematic grid of permanent sample plots and provides a reliable evidence-based assessment of the state and the development of Germany’s forests on national and federal state level in a 10 year interval. However, the data have yet been scarcely used for estimation on smaller management levels such as forest districts due to insufficient sample sizes within the area of interests and the implied large estimation errors. In this study, we present a double-sampling extension to the existing German National Forest Inventory (NFI) that allows for the application of recently developed design-based small area regression estimators. We illustrate the implementation of the estimation procedure and evaluate its potential for future large-scale operational application by the example of timber volume estimation on two small-scale management levels (45 and 405 forest district units respectively) over the entire area of the federal German state of Rhineland-Palatinate. An airborne laserscanning (ALS) derived canopy height model and a tree species classification map based on satellite data were used as auxiliary data in an ordinary least square regression model to produce the timber volume predictions. The results support that the suggested double-sampling procedure can substantially increase estimation precision on both management levels: the two-phase estimators were able to reduce the variance of the one-phase simple random sampling estimator by 43% and 25% on average for the two management levels respectively.

Use of partial-coverage UAV data in sampling for large scale forest inventories

The use of image-based three-dimensional data from unmanned aerial vehicles (UAV) has proven effective for forest inventories. However, limitations in the range of UAV operations hinder their use in large scale applications. Use of partial-coverage UAV data in combination with field plots may increase precision of field-based estimates of forest resource parameters and may offer a cost-effective alternative to wall-to-wall acquisition. In this study, data from UAV collected in systematically distributed blocks and combined with field plots in a two-phase design with hybrid inference (UAVHYB) were used to estimate mean volume and its precision (standard error) for a 7330ha forest area in Norway. Because in UAVHYB the field data do not necessarily need to come from a probability sample, the approach offers great flexibility in field data collection. The estimate of precision using UAVHYB was compared to two alternative inventory approaches differing in terms of sampling design and mode of inference, i.e., (1) single-phase probabilistic sampling relying only on field samples for which the design-based approach to inference using simple random sampling estimators was adopted (FIELDDB) and (2) a model-based approach independent from design assumptions for which wall-to-wall airborne laser scanning data were applied (ALSMB). Relative efficiency (RE), calculated as the ratio between the estimated variances of two different inventory approaches, was used as measure for improvement in variance for one approach over the other. Comparison of UAVHYB against FIELDDB revealed that the use of the former was up to four times more efficient than the latter (RE=4.4). This translates to a need for 4.4 times as many field plots under simple random sampling for a FIELDDB estimate to be equally precise as the UAVHYB estimate. For ALSMB the increase in efficiency compared to UAVHYB was limited (RE=1.6). The study also demonstrated that the precision under UAVHYB can be improved when including additional field data from other inventories to enhance the model. Cost estimates for each inventory approach were compared, revealing that UAV may be a cost-effective tool for large scale forest resource assessments.

Sampling Variance and Bias of the Wilks Conservative Estimate of Confidence Intervals

For evaluation of the uncertainty of nuclear power calculations, the Wilks approach has the appearance of an ideal tool. A conservatively estimated bound is obtained as the r’th most extreme model result, of a random sample of size determined by r. The methodology is noninvasive and simple and seems efficient and adequate. However, as this paper shows, these attributes come with a high price of large bias and substantial sampling variance. This jeopardizes its utilization as well as lowers its credibility and perceived efficiency. The unfortunate combination of random sampling and faithful estimation may result in a relative sampling uncertainty of the estimated bound(s) of no less than 100%. What is defined as credibility, i.e., the probability that the estimated bound is conservative relative to the true result, is well below the confidence relating the targeted bound(s) to the true result, which for the default application of the Wilks method translates into an expected failure rate of up to 10% (instead of 5%) of estimated bounds. To compensate for this deficit in credibility compared to the chosen level of confidence, adjustments of current practice are proposed. The application to modeling uncertainty is to be clearly distinguished from the original experimental sampling problem addressed by Wilks. Here, more is known but not utilized. A viable novel alternative based on so-called deterministic sampling with higher accuracy, precision, and efficiency will therefore be briefly discussed and illustrated.

Hybrid estimators for mean aboveground carbon per unit area

Carbon accounting is at the heart of efforts to mitigate the effects of climate change. One approach for estimating population parameters for live tree stem carbon entails three primary steps: (1) construction of an individual tree, allometric carbon model, (2) application of the model to tree-level data for a probability sample of plots, and (3) use of a probability-based (design-based) estimator of mean carbon per unit area for a population of interest. Compliance with the IPCC good practice guidance requires satisfaction of two criteria, one related to minimizing bias and one related to minimizing uncertainty. For this carbon estimation procedure, the portion of uncertainty attributed to the variance of the probability-based estimator of the population mean using the plot-level predictions is usually correctly estimated, but the portion attributed to the variance of the allometric model estimator is usually ignored. The result is that the total variance of the population mean estimator cannot be asserted to comply with the IPCC good practice criteria because not only is it not minimized, it is not even correctly estimated.Within the framework of what is coming to be characterized as hybrid inference, model-based inferential methods were used to estimate the variance of the tree-level allometric model estimator which was then propagated through to the variance of the probability-based estimator of mean carbon per unit area. This combined estimator, consisting of a model-based estimator used to predict a variable for a probability sample of a population followed by a probability-estimator of the population total or mean using the sample predictions, is characterized as a hybrid estimator. For this study, two probability-based estimators of the mean were considered, simple random sampling estimators and model-assisted regression estimators that used airborne laser scanning (ALS) data as auxiliary information. The variance of the allometric model estimator incorporated variances of distributions of diameter and height measurement errors, covariances of model parameter estimators, model residual variance, and variances of distributions of wood densities and carbon content proportions.The novel features of the study included the hybrid inferential framework, consideration of six sources of uncertainty including the variances of distributions of wood densities and carbon content proportions, use of ALS data with model-assisted regression estimators of the population mean, and use of confidence intervals for the population mean as the basis for comparisons rather than intermediate products such as model prediction accuracy. The primary conclusions were that the variance of the allometric model estimator was negligible or marginally negligible relative to the variance of the probability estimator when using species-specific allometric models and simple random sampling estimators, but non-negligible when using species-specific models and model-assisted regression estimators and when using a non-specific model with either estimator.

Some theoretical results concerning non parametric estimation by using a judgment poststratification sample

ABSTRACTIn this paper, some of the properties of non parametric estimation of the expectation of g(X) (any function of X), by using a judgment poststratification sample (JPS), have been discussed. A class of estimators (including the standard JPS estimator and a JPS estimator proposed by Frey and Feeman (2012, Comput. Stat. Data An.) is considered. The paper provides mean and variance of the members of this class, and examines their consistency and asymptotic distribution. Specifically, the results are for the estimation of population mean, population variance, and cumulative distribution function. We show that any estimators of the class may be less efficient than simple random sampling (SRS) estimator for small sample sizes. We prove that the relative efficiency of some estimators in the class with respect to balanced ranked set sampling (BRSS) estimator tends to 1 as the sample size goes to infinity. Furthermore, the standard JPS mean estimator, and Frey–Feeman JPS mean estimator are specifically studied and we show that two estimators have the same asymptotic distribution. For the standard JPS mean estimator, in perfect ranking situations, optimum values of H (the ranking class size), for different sample sizes, are determined non parametrically for populations that are not heavily skewed or thick tailed.

Efficient separate class of estimators of population mean in stratified random sampling

ABSTRACTIn this paper, efficient class of estimators for population mean using two auxiliary variates is suggested. It has been shown that the suggested estimator is more efficient than usual unbiased estimator in stratified random sampling, usual ratio and product-type estimators, Tailor and Lone (2012, 2014) estimators, and other considered estimators. The bias and mean-squared error of the suggested estimator are obtained up to the first degree of approximation. Conditions under which the suggested estimator is more efficient than other considered estimators are obtained. An empirical study has been carried out to demonstrate the performances of the suggested estimator.

Propagating uncertainty through individual tree volume model predictions to large-area volume estimates

The effects on large-area volume estimates of uncertainty in individual tree volume model predictions were negligible when using simple random sampling estimators for large-area estimation, but non-negligible when using stratified estimators which reduced the effects of sampling variability. Forest inventory estimates of tree volume for large areas are typically calculated by adding model predictions of volumes for individual trees at the plot level and calculating the per unit area mean over plots. The uncertainty in the model predictions is generally ignored with the result that the precision of the large-area volume estimate is optimistic. The primary objective was to estimate the effects on large-area volume estimates of volume model prediction uncertainty due to diameter and height measurement error, parameter uncertainty, and model residual variance. Monte Carlo simulation approaches were used because of the complexities associated with multiple sources of uncertainty, the non-linear nature of the models, and heteroskedasticity. The effects of model prediction uncertainty on large-area volume estimates of growing stock volume were negligible when using simple random sampling estimators. However, with stratified estimators that reduce the effects of sampling variability, the effects of model prediction uncertainty were not necessarily negligible. The adverse effects of parameter uncertainty and residual variance were greater than the effects of diameter and height measurement errors. The uncertainty of large-area volume estimates that do not account for model prediction uncertainty should be regarded with caution.

Indirect and direct estimation of forest biomass change using forest inventory and airborne laser scanning data

Remote sensing-based change estimation typically takes two forms. Indirect estimation entails constructing models of the relationship between the response variable of interest and remotely sensed auxiliary variables at two times and then estimating change as the differences in the model predictions for the two times. Direct estimation entails constructing models of change directly using observations of change in the response and the remotely sensed auxiliary variables for two dates. The direct method is generally preferred, although few statistically rigorous comparisons have been reported. This study focused on statistically rigorous, indirect and direct estimation of biomass change using forest inventory and airborne laser scanning (ALS) data for a Norwegian study area. Three sets of statistical estimators were used: simple random sampling estimators, indirect model-assisted regression estimators, and direct model-assisted regression estimators. In addition, three modeling approaches were used to support the direct model-assisted estimators. The study produced four relevant findings. First, use of the ALS auxiliary information greatly increased the precision of change estimates, regardless of whether indirect or direct methods were used. Second, contrary to previously reported results, the indirect method produced greater precision for the study area mean than the traditional direct method. Third, the direct method that used models whose predictor variables were selected in pairs but with separate coefficient estimates and models whose predictor variables were selected without regard to pairing produced the greatest precision. Finally, greater emphasis should be placed on the effects of model extrapolations for values of independent variables in the population that are beyond the range of the variables in the sample.

ROBUSTNESS OF WILKS' CONSERVATIVE ESTIMATE OF CONFIDENCE INTERVALS

The striking generality and simplicity of Wilks’ method has made it popular for quantifying modeling uncertainty. A conservative estimate of the confidence interval is obtained from a very limited set of randomly drawn model sample values, with probability set by the assigned so-called stability. In contrast, the reproducibility of the estimated limits, or robustness, is beyond our control as it is strongly dependent on the probability distribution of model results. The inherent combination of random sampling and faithful estimation in Wilks’ approach is here shown to often result in poor robustness. The estimated confidence interval is consequently not a well-defined measure of modeling uncertainty. To remedy this deficiency, adjustments of Wilks’ approach as well as alternative novel, effective but less known approaches based on deterministic sampling are suggested. For illustration, the robustness of Wilks’ estimate for uniform and normal model distributions are compared.